Procedure for the elimination of interference in a radar unit of the FMCW type

ABSTRACT

This invention concerns a procedure for the elimination of interferences, such as pulses and linear chirps, in a radar unit of the FMCW type. According to the procedure, the useable signal in the form of a beat signal, is subjected to time-frequency division of the type STFT for division of the signal into narrow-band frequency bands. Interference is detected and eliminated in each frequency band, after which the time signal freed from interference and its Discrete Fourier Transform, DFT, are calculated from the time-frequency division in narrow-band frequency bands.

BACKGROUND OF THE INVENTION

This invention concerns a procedure for the elimination of interference,such as pulses and linear chirps, in a radar unit of the FMCW type withlinear frequency sweep, where the transmitted and received signals arecombined to form a useable signal in the form of a difference signal.This difference signal is commonly termed the beat signal, and itincludes a wave for each target, where the frequency, amplitude andphase of the wave contain information about the target. The procedurecan be used in the field of mobile radar, but it can also be used forother FMCW radar applications.

The principle for linear FMCW radar is well-known, see for exampleSkolnik, Introduction to Radar Systems, 2nd Ed., McGraw-Hill 1980,chapter 3. Technical advances have resulted in an increased use of FMCWradar units, which will not be considered further here. A linear FMCW(Frequency Modulated Continuous Wave) radar unit, in principle, works asfollows:

A frequency sweep controls an oscillator with a variable frequency sothat the transmitted frequency varies periodically. Each period hasprincipally three parts, namely a constant base frequency extent, alinear frequency sweep extent and a rapid return to base frequencyextent. The linear frequency sweep extent is the time when the radarunit is “carrying out useful work” and often constitutes 70-80% of thetotal time (work factor 0.7-0.8).

For the sake of simplicity in the discourse below the radar unit and itstarget are considered stationary. In the case of moving targets ormoving radar units the Doppler effect also comes into play. For mostactual FMCW systems, however, the Doppler effect only involves a minorcorrection.

The propagation time from the radar unit to a target and back again istypically a few microseconds. A signal received from a target thereforehas the frequency that was transmitted a certain time previously. Sincethe frequency is swept this is not the same frequency that is beingtransmitted. The received frequency also has a linear frequency sweep.The received frequency sweep and the transmitted frequency sweep areparallel with a time-displacement equal to the propagation time.Therefore for a fixed target the difference in frequency between thetransmitted and received signal will be constant. This constantfrequency difference is given by the product of the propagation time tothe target and the gradient of the frequency sweep expressed asfrequency per unit of time.

Signal processing in a linear FMCW radar unit consists principally ofthe transmitted and received signals being combined, so that thedifference signal (the beat signal) is generated. This signal is the sumof a number of sine waves, where each sine wave represents a radartarget. The sine waves have different frequencies, amplitudes andinitial phases. Typically a large amplitude corresponds to large target,and a high frequency corresponds to a target at a great distance. TheDoppler effect (due to the relative speed) mainly affects the initialphases.

In order to determine what targets are being observed and their sizesand relative speeds, the difference signal is frequency-analysed. Thefrequency analysis is best carried out digitally. The difference signalis passed through an anti-alias filter and then sampled at a constantsampling rate. Thereafter the sampled signal is multiplied by a windowfunction to reduce the amplitude of the signal at the start and end ofthe sampling period and the product is sent to a signal processor thatcarries out a Discrete Fourier Transform, DFT, usually with a fastalgorithm, known as an FFT, Fast Fourier Transform. The FourierTransform is generally complex but for a real time signal (differencesignal) it has a certain degree of symmetry. In order to be able to useFFT algorithms the number of samples is usually selected as a power oftwo (256, 512, 1024 . . . ). 256 samples give 256 FFT coefficients, butif the signal is real the symmetry means that of these 256 values only128 (actually 129) are independent.

With application of Fourier Transform, for example by FFT, the signal isdivided up into a number of discrete frequency components, such assines. Each frequency corresponds, as indicated, to a distance. Theamplitude of a complex FFT coefficient is a measurement of the radartarget area (the received power) for the target in the correspondingfrequency window (distance window). The FFT performs what is known as acoherent integration of the target signal, which is advantageous. Thesubsequent signal processing in the system is carried out digitally onthe calculated FFT coefficients.

It can be shown that the nominal width of a distance window is inverselyproportional to the change in frequency of the linear FMCW sweep duringthe sampling period. For a distance resolution of 1 m a change infrequency of 150 MHz is required. In order to change the distanceresolution, the gradient of the frequency sweep can, for example, bechanged while retaining the same sampling time.

The sampling rate limits the frequencies of the beat signal that can bestudied and thereby the total observed distance. The width of this“useable band” that lies parallel to the linear FMCW sweep is often lessthan 1 MHz.

A linear FMCW radar unit can be subjected to interference if it receivessignals other than its own transmitted signals reflected from varioustargets. The radar unit can be subjected to interference from otherradar units, including pulse radar units, pulse compression radar unitsand other FMCW radar units that are operating at the same time.

A pulse present during the sampling period has a very short extent inthe time domain and is very broad-band in the frequency domain. A stronginterfering pulse only affects a few samples of the beat signal but canaffect all the frequencies or frequency bins in the Fourier Transform.The “noise level” in the Fourier Transform appears to be increased, sothat small targets can be masked by the interference.

A very common form of interference is what is known as a chirp, wherethe wave form causing the interference moves with a linear frequencythrough the useable band of the FMCW radar unit. Such chirps aregenerated by a pulse compression radar unit, and also by another FMCWradar unit if that unit's transmitted wave form during the base andreturn extents enters the first unit's useable band during its samplingperiod. The third extent, the linear frequency sweep, can also generatea chirp if the frequency sweep of the radar unit causing theinterference has a different gradient from the frequency sweep of thefirst radar unit, e.g. because the radar unit causing the interferencehas a different distance resolution.

Interference in the form of a linear chirp is always broad-band infrequency, but can also have a considerable extent in time and causeinterference to the whole FFT and affect a very large part of thesampled time signal.

There are also short chirps that can hardly be distinguished frompulses. The chirps that are caused by the base extent or return- extentof an interfering FMCW radar unit are of this type.

Interference of short duration such as short pulses or rapid chirps cangenerally be detected and eliminated in the sampled time signal. and anFFT without interference can then in general be reconstructed. A chirpinterference with a large extent in both the time domain and in theFourier domain can, however, not be eliminated by any simplemanipulation of the time signal without negative consequences for theFFT.

BRIEF SUMMARY OF THE INVENTION

According to this invention a procedure is proposed for eliminatinginterference in radar units of the FMCW type that is capable ofeliminating interference with a large extent in both the time domain andFourier domain. The method according to the invention is characterisedby (1) the beat signal being subjected to time-frequency division fortime-local resolution, (2) by the interference being detected andeliminated separately in each frequency band individually, after which(3) the time signal free of the interference and its Discrete FourierTransform, DFT, are calculated from the time-frequency resolution.

The sampled beat signal, the time signal, lies completely in the timedomain. The samples give a resolution in time but no resolution at allin frequency. The FFT is a description of the same signal in the Fourierdomain. The FFT gives a good resolution in frequency, but no resolutionat all in time. Interference, e.g. a chirp, present for a short time ispoorly visible in the Fourier domain. Information about the position ofthe interference is to be found mainly in the phases of the complex FFTvalues and not in the amounts or amplitude.

What is known as a time-frequency resolution makes it possible to havecertain (coarse) resolution of the signal in the time domain and in theFourier domain. A known time-frequency resolution is the Wigner-VilleTransform, which is what is known as a quadratic transform and thereforecreates false cross-modulation products, see Mayer, Wavelets, Algorithms& Applications, SIAM, Philadelphia, 1993. Another known time-frequencyresolution is what is known as the wavelet transform, see the book byMayer, or Rioul/Vetterli, Wavelets and Signal Processing, IEEE SignalProcessing Magazine, October 1991, that makes a “musical” frequencydivision. The frequency division is into different scalesor “octaves”.For high frequencies the frequency resolution (expressed in Hz) iscoarser but the time resolution is finer.

The expressions “time-frequency analysis”, “time-frequencydecomposition” (cf. the above book by Mayer), “time-frequencydistribution” and “time-frequency representation” (cf. the references inthe above paper by Rioul/Vetterli) of a signal, leading to a‘time-frequency resolution”, are all in common use and mean essentiallythe same thing: some expressions stress the work done (“analysis”),other the result of the work (“decomposition”, “representation”,“resolution”), still other the particular methods used (“distribution”).Here the expressions are used as synonyms.

For the application of interference attenuation in FMCW radar unitsthere is proposed, however, mainly the simplest time/frequencyresolution, Short Time Fourier Transform, STFT, described in theRioul/Vetterli reference above. In STFT the time signal is divided intoshort sections that can overlap. Each section of signal is multiplied bya window function and a Discrete Fourier Transform is calculated. TheSTFT provides a frequency decomposition for every small part of the timesignal and is a time-frequency decomposition. After the elimination ofinterference in each frequency band individually, the original timesignal is calculated from the STFT. The STFT can therefore usefullycontain redundant (overlapping) information.

In this connection it is useful to point out that an FMCW radar unit isthe only common type of radar unit where a target corresponds to astanding wave with a certain frequency thus fulfilling the conditionsfor application of normal Fourier analysis with band-pass filter or DFT(FFT).

Detection of interference in each frequency band can advantageously becarried out by methods suitable for the detection of short durationinterference.

In one suitable version of the method, the detection of linear chirpsand pulses is carried out by methods for detecting straight lines inimages, for example so that interference patterns in the form ofstraight lines not parallel with the time axis are identified, the timeswhere interference lines intersect the different frequency bands of theSTFT are determined and the interference is eliminated separately ineach affected frequency band. Methods for detecting straight lines inimages are known from image processing, see for example Gonzalez/Woods,Digital Image Processing, Addison-Wesley, 1992. A Hough Transform can beused for the detection of the straight lines.

In another suitable version of the method in accordance with theinvention, the beat signal is filtered in association with thetime-frequency resolution in narrow frequency bands of the signal inorder to increase the sensitivity of the detection. The filter can bedetermined using adaptive methods. In one favorable version, the filteris applied on one or more of the narrow-band frequency bins of thetime-frequency resolution.

In yet another suitable version of the method in accordance with theinvention, the beat signal or useable signal is reconstructed after theelimination of interference by extrapolation from samples withoutinterference, in one or more of the narrow-band frequency bands of thetime-frequency resolution.

STFT-time-frequency resolution for the detection of interference, theelimination of interference and synthesis of the useable signal has manyadvantages, particularly for chirps. The advantages consist in generalof two characteristics. The first is that a chirp in each frequency binin the STFT is of short duration and can therefore bedetected/eliminated by the same methods as, for example, pulses. Thesecond is that chirps are narrow-band in each frequency band in the STFTand can therefore be described (reduced to zero/extrapolated) usingsimple polynomials of already known structure.

BRIEF DESCRIPTION OF SEVERAL VIEWS OF THE DRAWINGS

The method according to the invention will be described below in greaterdetail with reference to the enclosed figures, where:

FIG. 1 shows diagrammatically the principle for how a linear FMCW radarunit works and can be modified in accordance with the invention.

FIG. 2 shows examples of suitable frequency sweeps in a time-frequencydiagram.

FIG. 3 shows samples of a simulated FMCW beat signal with Gaussian noiseand interference.

FIG. 4 shows the absolute value of the FFT for the beat signal in FIG.3.

FIG. 5 shows the result of a time-frequency analysis of the beat signalin FIG. 3.

FIG. 6 shows the absolute value of the FFT for a beat signal in FIG. 3without interference.

DETAILED DESCRIPTION OF THE INVENTION

The radar unit shown in FIG. 1 includes a transmitter 1 and a receiver2. An antenna 3 is connected to the transmitter and the receiver via acirculator 4. In the transmitter there is an oscillator control device 5connected to a variable frequency oscillator 6. The frequency sweep fromthe oscillator control device 5 controls the oscillator 6 so that asignal is generated with periodically varying frequency. The signal istransmitted by the antenna 3 via a directional coupler 7 and thecirculator 4. The period of a frequency sweep, see FIG. 2, hasprincipally three parts in the form of a constant base frequency extent30, a linear frequency sweep extent 31 and a quick return extent 32. Theoscillator 6 can work within the Gigahertz range, e.g. 77 GHz. Thereflected signal received by the antenna 3 is taken via the circulator 4to a mixer 8, where the reflected signal is combined with thetransmitted signal. After amplification in the amplifier 9 and filteringin the filter 10 a difference signal or beat signal is obtained. Thebeat signal is used as the basis for the subsequent signal processing,for detecting and eliminating interference and synthesis of the useablesignal without interference in a processor block 11 that can alsocontain what is known as an FFT processor 11′.

An example of how the time-frequency resolution allows the analysis of adifference signal with interference is shown in FIGS. 3-6.

FIG. 3 shows 1024 samples of an FMCW beat signal (time signal) that issimulated as a number of sine/cosine signals+Gaussiannoise+interference. It is difficult by eye to locate and accuratelycharacterise the interference.

FIG. 4 shows the absolute value of the FFT for the beat signal in FIG.3. This illustration reveals four distinct peaks 12, 13, 14 and 15 abovea high noise base. Each peak 12-15 corresponds to a target. It is notpossible to characterise the interference from FIG. 4.

FIG. 5 shows the result of a time-frequency analysis of the beat signalin FIG. 3. FIG. 5 is the result of a STFT performed on batches of 64samples at a time with overlaps. From FIG. 5 it appears directly fromthe V 16 that can be seen in the center of the signal that theinterference is a linear chirp. The explanation for the chirp being a Vand not just a line is that the FFT analysis cannot distinguish betweenpositive and negative frequencies. The dominant peaks in the spectrumappear as horizontal bands 17-21 corresponding to standing sine waveswith constant frequency. In FIG. 5 the frequency resolution is quitecoarse and the two peaks 14, 15 in FIG. 4 move partly together into asingle broad band 19, 20. A horizontal band 21 at approximately0.8*Nyquist frequency does not correspond to any peak in FIG. 4.

By studying the simulated signal without. interference and withoutchirps, shown in FIG. 6 as the absolute value of the FFT, a fifth peak22 appears associated with the band 21 corresponding to a fifth target.In FIG. 4 this peak is completely submerged by the interference.

One of the great advantages of time-frequency resolution (STFT) for theelimination of interference in FMCW signals can be seen by comparingFIG. 5 and FIG. 3. In FIG. 3 the interference is long. The length of theinterference corresponds to the projection of the V on the horizontaltime axis in FIG. 5. In each frequency window in FIG. 5 the interferenceis, on the other hand, relatively short.

By processing each frequency bin individually in an STFT, chirps can bedetected and eliminated using the same methods that are used forinterferences of short duration pulses. The V 16 in FIG. 5 can bedetected and eliminated and the horizontal bands, the useable-signals,can be reconstructed, after which the reconstructed time signal withoutinterference and FFT without interference can be calculated from theSTFT. This is the principle behind the method according to theinvention.

FIG. 5 shows that a chirp appears as a V, labeled 16, in an STFTanalysis. In the same way a pulse appears as a vertical line localizedin time but broad-band. The useable signals are, however, horizontallines. It is therefore possible to detect interference of a pulse or alinear chirp by looking in an STFT image for lines that are not parallelwith the time axis. Such methods are known from image processing, seefor example the Gonzalez/Woods reference mentioned above. A suitablemethod in this connection is described in chapter 7 in this referenceand is based on what is known as a Hough Transform.

In the following we discuss in greater detail the principles forfiltering the useable signal.

The useable signal in an FMCW radar unit, i.e., the signal thatcorresponds to the actual target, is a sum of sine waves. A signalconsisting of a single sine wave, sampled with constant frequency, has asimple linear relationship between samples. Assume that the signal canbe written as sin(ω*t+ψ). Between two samples the phase angle of thesine wave thus changes by the angle ωT=θ, where T is the samplinginterval. In accordance with the trigonometric identity

sin(α+θ)+sin(α−θ)=2*cos(θ)*sin(α)

it is then the case for three successive samples of the signal that:

x(n+1)+x(n−1)=2*cos(θ)*x(n)

Note that this is applicable regardless of the amplitude of the signal.This linear relationship can be interpreted in various ways:

a) If the signal is passed through an FIR filter (Finite ImpulseResponse) with the coefficients [1−2*cos(θ) 1], the output signal y fromthe filter will be identical to 0:

y(n)=x(n)−2*cos(θ)*x(n−1)+x(n−2)

It is possible therefore to strongly attenuate the signal with a singleFIR filter with constant coefficients.

b) If the relationship is instead written:

x(n+1)=2*cos(θ)*x(n)−x(n−1)

it can be seen that the next sample can be predicted by a linearcombination of the immediately preceding samples.

For a signal that consists of several sine waves with distinctfrequencies corresponding filters can be created by multiplication ofsecond order FIR filters. A signal that is the sum of four differentsine waves, i.e. an FMCW signal with four strong targets, can thus bereduced to zero by an FIR filter of order 8 and a sample can bepredicted linearly from the 8 preceding ones.

For a general FMCW signal these relationships are approximate, but thefollowing can be said in general to apply:

1. It is possible to strongly attenuate an FMCW signal by means of asuitable linear FIR filter of a suitable order.

2. It is possible to predict linearly an FMCW signal using a suitablelinear relationship of a suitable order.

The application of point 1 is that the sensitivity of the detection ofinterference is greatly increased if the useable signal is pre-filteredin a suitable way. In FIG. 5 this corresponds to the horizontal bandsbeing filtered away. Only the interference then remains against a weakbackground. This permits the detection of interference with an amplitudethat is much lower than that of the useable signal, e.g. a signal thatis completely invisible by analysis of the amplitudes in FIG. 3 but thatstill increases the noise base in the FFT in FIG. 6.

Point 2 makes it possible to interpolate the useable signal past a shortsection with interference, which will be described in greater detaillater on.

A “suitable” filter can be calculated in various ways, or calculated asan adaptive filter. Both problems according to point 1 and point 2 aboveare known from adaptive signal processing, see for example Haykin,Adaptive Filter Thoery, 2^(nd) Ed., Prentice-Hall 1991. The coefficientscan be determined by the usual algorithms, e.g. LMS, normalized LMS,RLS, etc, see in particular chapters 9 and 13 in the above reference.

By adaptive determination of a filter it is often possible to use thefact that the radar antenna has turned, although only a fraction of abeam width, since the previous FMCW frequency sweep. The dominant sinewaves in the signals from two subsequent FMCW sweeps have, as a result,almost the same frequency and almost the same amplitude. The startvalues of the adaptation can therefore be selected as the end valuesfrom the adaptation during the previous FMCW sweep.

It is also an important observation that in each frequency band in aSTFT division of the signal the filters are very simple. In eachfrequency band the signal is narrow-band and the middle frequency of thewindow is known. This means that the phase shift between two successivesamples is known and just a second order filter has a very good effect.

In the following the synthesizing of the useable signal is discussed.

A usual method of attenuating interference is to detect interference,e.g. a pulse, by the signal amplitude being unusually large and then tocarry out clipping of the signal, preferably to the level 0. This can initself eliminate the interference, but adversely affects the FFT by alsoaffecting the useable signal.

The precondition for an FFT is that the sample is sampled equidistantlyover a suitable period. Clipping of the signal removes samples. It canbe said that the time base of the useable signal is affected. Aconsequence is that distinct targets are widened in the Fourier domain,which among other things can result in a reduction in the resolution.

A very useful method is to follow up the interference elimination by asynthesis of the useable signal. Here point 2 above can be used. Thesynthesis can consist of an extrapolation (one-ended) or interpolation(two-ended) of the signal based on values without interference. Such asynthesis can result in a dramatic improvement in the reconstruction ofthe FMCW signal without interference and its FFT.

The polynomial of the interpolation/extrapolation can as mentioned abovebe determined adaptively or in another way. The interpolation isparticularly simple if the signal is narrow-band, as an interpolationpolynomial of low order is usually sufficient.

The interpolation/extrapolation is numerically sensitive, among otherthings on account of the fact that the roots of the polynomial of theextrapolation lie on or near the unit circle and numerical interferencetherefore does not die out, and can also for other reasons only becarried out over short sections of time. It is therefore not possiblesimply to interpolate/extrapolate past a chirp of a certain length.

This problem can be solved by carrying out an STFT on the signal withinterference in accordance with this invention. In each frequency windowthere will then be a chirp of only a short duration. In addition thesignal components in each frequency window are narrow-band, which inaccordance with the above makes the interpolation/extrapolation muchsimpler.

What is claimed is:
 1. A method for the elimination of interference in aFMCW radar unit wherein transmitted and received signals are combined toform a difference signal; said method comprising the steps (a)performing a time-frequency resolution of the difference signal to formindividual frequency bands of said difference signal; (b) detecting andeliminating interference separately in each of said frequency bands toform interference-free frequency bands; and (c) constructing aninterference-free time signal from said interference-free frequencybands.
 2. The method of claim 1 which includes the further step of: (d)calculating a Discrete Fourier Transform (DFT) from saidinterference-free time signal.
 3. The method of claim 2 wherein saidtime-frequency resolution is a Short Time Fourier Transform (STFT) andwherein said DFT is a Fast Fourier Transform (FFT).
 4. The method ofclaim 1 wherein said time-frequency resolution is a Short Time FourierTransform (STFT).
 5. The method of claim 1, wherein said interferencecomprises chirps and pulses, and said interference detecting employsprocedures to detect straight lines in images.
 6. The method of claim 5,wherein the straight lines which are detected are lines which are notparallel with a time axis, and the method further comprises eliminatinginterference corresponding to the detected lines in each of pluralfrequency bands.
 7. The method of claim 5 which includes applying aHough transform for straight-line detection.
 8. The method of claim 7which includes the further step of: (d) calculating a Discrete FourierTransform (DFT) from said interference-free time signal.
 9. The methodof claim 8 wherein said time-frequency resolution is a Short TimeFourier Transform (STFT) and wherein said DFT is a Fast FourierTransform (FFT).
 10. The method of claim 9, wherein said step (b)further comprises pre-filtering frequency bands corresponding to saiddifference signal, to increase the sensitivity of detection.
 11. Themethod of claim 10, wherein said step (b) further comprises calculatingan adaptive filter for performing said pre-filtering.
 12. The method ofclaim 11, wherein said filter is applied to at least one frequencywindow of a frequency band formed by said time-frequency resolution. 13.The method of claim 12, wherein said step (c) comprises extrapolatingfrom interference-free samples.
 14. The method of claim 1, wherein saidstep (b) further comprises pre-filtering frequency bands correspondingto said difference signal, to increase the sensitivity of detection. 15.The method of claim 14, wherein said step (b) further comprisescalculating an adaptive filter for performing said pre-filtering. 16.The method of claim 15, wherein said filter is applied to at least onefrequency window of a frequency band formed by said time-frequencyresolution.
 17. The method of claim 1, wherein said step (c) comprisesextrapolating from interference-free samples.